Grace McDonnell's parents gave one of her paintings to Barack Obama. The seven-year-old, who dreamed of being a painter, was shot dead in her classroom last month.

The picture now hangs in the president’s study as a reminder to act. Even in a country as accustomed to gun violence as America, the murder of 26 people, including 20 children, in a Newtown, Connecticut school last month was especially shocking.

On that day a tearful Mr Obama said serious action was needed to prevent any more tragedies.

On January 16th Mr Obama, along with Vice-President Joe Biden, who headed the president’s gun task-force, unveiled the most sweeping gun-control proposals Washington, DC has seen for two decades. Whether they will be implemented or make much difference is another matter.

The president’s plan was inspired not just by the children killed in Newtown, but by the more than 30,000 deaths caused by guns every year. Mr Obama announced 23 executive orders, which do not need congressional approval.

These include strengthening the system of background checks (which is notoriously ineffective) and providing more support to law-enforcement agencies. Another order seeks to make schools safer by ensuring that each one has an emergency management plan (most of them, including the Newton one, already do).

But Mr Obama will need congressional backing for the main part of his plan: a proposal to renew an assault-weapons ban that went into effect in 1994 but expired ten years later. The ban would include, as it did back in 1994, a ban on high-capacity ammunition magazines, containing more than ten rounds. The trouble is that ban, especially the magazine part of it, proved impossible to enforce.

States, meanwhile, have jumped the gun. Andrew Cuomo, New York’s governor and a gun-owner, signed the NY Safe Act on January 15th. The state, which already had strong gun laws, has now banned military-style assault weapons, and has mandated universal background checks, including on buyers of ammunition.

Martin O’Malley, Maryland’s governor, is about to introduce a sweeping gun-control package which echoes many of New York’s measures. Colorado’s governor has called for background checks for private gun sales, which are currently exempt. Deval Patrick, the governor of Massachusetts, wants to limit gun sales to one a month. Of course, one can do quite a lot of damage with one gun a month.

Cities, too, are taking a stand. Since the Newtown shooting, more than 100 more mayors have joined Mayors Against Illegal Guns, the 800-strong coalition founded by Michael Bloomberg, New York’s mayor.

Welcome as these state and city actions are, without federal backup they are not much use. They may also be vulnerable to recision by the Supreme Court.

Would-be killers need only cross state lines to places with weak gun laws to get access to weapons. Nor is it clear whether the president’s plan would have prevented the Newtown massacre. There, the shooter did not have a background check; he used his mother’s guns.

Mr Obama faces steep opposition, and not just from congressional opponents: even his fellow Democrat, Harry Reid, the majority leader of the Senate, has indicated that the assault-weapons ban will be a hard sell. While states like New York and California are moving to strengthen gun laws, other states are doing the opposite.

Lawmakers in Arizona and Texas, for instance, intend to introduce bills that would loosen gun restrictions. A Kentucky sheriff has said he will not enforce any new gun laws that he deems unconstitutional.

Most shockingly, gun sales have soared in recent weeks. In the month since the Newtown shooting 250,000 more people have joined the National Rifle Association, which has vowed to oppose the ban.

The group is getting so cocky that it launched a free shooting app this week. For an extra 99 cents, players can use a MK-11 sniper rifle to shoot coffin-shaped targets.